<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_8.html#V7" title="CAT_8:attr.7">with_binary_products</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font>  st  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b3">c</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Olive" title="b2">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:66"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
(  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:66"/>
( <font color="Maroon" title="c2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">b</font>, <a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>), <a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:66"/>
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#D10" target="_self" onmouseover="rs('cat_8/D10')" onmouseout="rh()">Def10</a>, <a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
